Answer Happy

Please clearly write the proof process of the question,thanks
6. (15 points) Prove that (1) (5 points) Prove that if n € Z is even, then n² + 3n+ 5 is odd. (2) (5 points) Let a € Z. Prove that if 2 | a and 5 | a, then 10 | a. X (3) (5 points) Define a real number x to be an integer root if x = m for some m € Z and k € Z with k ≥ 0. Prove that if x and y are both integer roots, then so is x · y.